Question

A collection of dimes and nickels is worth 3.30. if there are 42 coins in total how many of each kind of coin are there?

Answer 1

To find the number of dimes and nickels in the collection of coins worth $3.30 with 42 coins in total, we can set up a system of equations and solve for the variables.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let's denote the number of dimes as 'd' and the number of nickels as 'n'.

We can write two equations based on the given information:

d + n = 42 (equation 1)

0.10d + 0.05n = 3.30 (equation 2)

To solve this system, we can multiply equation 1 by 0.05 to get:

0.05d + 0.05n = 2.10 (equation 3)

Now, subtract equation 3 from equation 2:

0.10d + 0.05n - (0.05d + 0.05n) = 3.30 - 2.10

0.10d - 0.05d = 1.20

0.05d = 1.20

d = 24

Substitute the value of d into equation 1:

24 + n = 42

n = 42 - 24

n = 18

Therefore, there are 24 dimes and 18 nickels in the collection.

Answer 2

1 nickels =$0.05
1 dime= $0.1
let the number of nickels be x and that of dimes be y.
total number of coins is given by:
x+y=42
hence:
y=42-x.......i

total amount of cash will be:
0.05x+0.1y=3.30.........ii
substituting i in ii we get:
0.05x+0.1(42-x)=3.30
0.05x+4.2-0.1x=3.3
-0.05x=-0.9
x=-0.9/(-0.05)
x=18
hence the the number nickels is x=18, the number of dimes will be y=42-x=42-18=24